Decomposition of tripartite graph states

Unlike bipartite states, multipartite states have no known simple method to fully characterize entanglement, and itis an interesting problem if such characterization is possible. We shed light on this problem by presenting a methodto decompose tripartite graph states into Bell pairs and GHZ states through a series of Clifford operations in eachsubsystem, and hence showing that entanglement of tripartite graph states can be fully characterized with 4 numbers;the number of Bell pairs between each pair of subsystems and the number of GHZ states shared by all subsystems.